When ‘$\,x\in\mathbb{R}\,$’ appears after the word ‘let’,
then the word ‘is’ is dropped,
and the word ‘be’ is inserted in its place.
Possible memory device: Let it be!

For all
[beautiful math coming... please be patient]
$\,x\in\mathbb{R}\,$

is read as:

‘For all ex in arr’
or
‘For all real numbers ex’

The phrase ‘For all $\,x\in\mathbb{R}\,$’ is always followed by something else,
which supplies the verb.
For example, you might see: For all $\,x\in\mathbb{R},\ \ x + 2 = 2 + x\,$.
Therefore, in this context, the words ‘is’ or ‘be’ are dropped,
and nothing is inserted in their place.